Dr. David J. Pearce

Understanding why Union Types are useful

The Whiley programming language uses union types as a way of combining types together.  Here’s a simple example to illustrate:

function indexOf(string str, char c) => null|int:
    for i in 0..|str|:
       if str[i] == c:
          return i // found a match
    // didn't find a match
    return null

Here, the type null|int is a union type — i.e. the union of types null and int. This means a variable of type null|int can hold any valid int or null. In this example, I’m using null to signal that the character c was not found in the string str. More formally, we can imagine types as sets where int is the set of all integers, and null is the singleton set containing the special value null. Then the union type null|int can be thought of as the set union of int and null.

This type null|int may seem familiar. In fact, it’s roughly equivalent to the Java type java.lang.Integer. As you may know, reference types in Java may hold the null as well as a valid object reference. A critical mistake in the design of Java (in my opinion) was to allow potentially null references to be dereferenced and, hence, the possibility of NullPointerExceptions. The design of Whiley contrasts with this, where union types provide an elegant solution. Specifically, a variable of type null|intcannot be treated as an int (i.e. you cannot perform arithmetic on it, etc). Instead, we must first check whether it actually is an int (or not) using a runtime type test. The following illustrates:

function replaceFirst(string str, char old, char repl) => string:
    idx = indexOf(str,old)
    if idx is int:
        str[idx] = repl
    // return potentially updated string
    return str

Here, the replaceFirst() function is replaces the first occurrence of a given character with an alternative. It uses indexOf() to find the first occurrence, and assigns the result to idx on Line 2. At this point, we cannot immediately perform the assignment str[idx]=repl (and, if we attempted this the compiler would give an error). This is because, immediately after Line 2, the variable idx has type int|null. However, on the true branch of the type test idx is int, the compiler automatically retypes idx to have type int and, hence, the assignment on Line 4 is safe.

Inheritance versus Union Types

Object-oriented languages use inheritance of classes (or interfaces) as a way to construct data types with commonalities.  In statically typed languages (like Java or C#), a common complaint is that this leads to “rigid” class hierarchies which (perhaps surprisingly) restrict how classes can be reused.  To understand this better, let’s consider a concrete example in Java:

abstract class Bytecode {
   abstract int stackDiff();

interface Branch { String target(); }

class Store extends Bytecode { ... }

class Goto extends Bytecode implements Branch { ... }

This is a simplification of a library I created for generating Java Bytecode in the Whiley compiler. Obviously, I’ve stripped out a lot of stuff for simplicity. However, we can see that every Bytecode has the method stackDiff() in common. Furthermore, I also wish to group other bytecodes together. For example, branching bytecodes (e.g. goto, ifeq, etc) have their destination target (which is a label) in common. To implement this, I’ve use a number of supplementary interfaces (e.g. Branch above). This is pretty flexible and allows me to describe lots of different groupings of the bytecodes.

Anyone who knows much about Java Bytecode will know that there are a large number of different bytecode groupings which are useful. For example, we might want to group bytecodes together that occupy a single byte in a class file (e.g. ineg, pop, dup, return, etc). Or, we might want to group together bytecodes which operate on int values (e.g. iadd, ificmp_eq, ireturn, etc). In fact, there are so many possible groupings that it is essentially impossible for the library designer (me, in this case) to implement them all up front as separate interfaces. The problem is, once we’ve defined a given class (e.g. Goto above), we’re stuck with those interfaces it does (or doesn’t) implement. In other words, we can’t group our bytecodes differently after the fact.

Now, union types provide an alternative approach which is both simple to understand and more flexible. Let’s rewrite the above in Whiley:

type Store is {
  int stackDiff(),

type Goto is {
  int stackDiff(),
  string target(),

type Bytecode is Store | Goto | ...
type Branch is Goto | ...

As we can see, grouping of bytecodes can be performed using union types. Furthermore, any union of records exposes fields common across all members. Therefore, if all bytecodes provide the stackDiff() method, then we can call this method whenever we have a variable of Bytecode type. The key here is that the groupings are independent of the individual components. Thus, we can define other groupings after the fact whenever we wish (e.g. in client code, etc).

More on Groupings

My use of union types above is not quite identical to the original Java code. That’s because the Bytecode type is fixed at its definition and cannot be extended. In contrast, the Java Bytecode class can be arbitrarily extended with new bytecodes. However, we can get a similar effect in Whiley by using another feature called structural typing. For example, we could define Bytecode as { int stackDiff(), ... }. Here, the ... is significant and indicates an open record (i.e. one which may have other fields not listed). Then, any record type which has the method int stackDiff() is automatically a subtype of Bytecode.

We can think of union types as providing closed (i.e. fixed) groupings of types, whilst structural subtyping provides open (i.e. extensible) groupings of types.  Taken together, these provide an interesting alternative mechanism for defining data types (compared with classical inheritance).  Closed groupings are used in situations where you know exactly what types you have, and e.g. you want the compiler to check you’ve covered all cases.  In contrast, open groupings are used when you want to provide an extension point for client code.  This provides a neat separation of the two different use cases, compared with e.g. Java where you only have inheritance to use.

Anyhow, that’s all for now!